This info from the Outward Bound Wilderness First Aid Handbook. The antivenin for pit vipers-- rattlers, cottonmouth and copperheads is the same, Coral snakes require a different antivenin. That snake is the only one in the US that needs distinguishing, others will show fang marks. The Coral with its short fangs, needs to do a bit of chewing before enough venom is introduced, so yank him off quickly, its venom may not display symptoms for several hours. The advice is to splint the limb to prevent movement but only if it won't delay evacuation time. Remain calm, keep the heart rate from soaring and pumping that stuff around quicker. In preparation for swelling remove anything that may constrict, jewelry etc. Apparently nothing has been proven to be effective other than antivenin. No compression, no icing, no tourniquets, no slicing and suction etc for pit vipers. A compression wrap between the bite of a coral snake and the heart MAY be helpful in some cases, as you're dealing with a pretty potent neurotoxin(isolating its circulation might do something)as opposed to tissue toxins of the pit vipers (with the exception of the Mojave rattler which contains a systemic neurotoxin as well)
Basically, walk out slowly if that's your mode. There is some time as others have said. Antivenin can apparently only be given at a hospital due to rare cases of extreme allergic reactions. It's best to inform the closest hospital asap if possible so the proper antivenin can be acquired by the time you're there(it may have to be flown in from somewhere). I can't locate the source for it but I think keeping the bite lower than the heart is the idea, gravity working to keep the venom in the extremity(if it's in an extremity). Someone may know better. Apparently, fatalities in the states are extremely rare.